Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #61049 |
| automorphism | ? |
| homology | Abelianization (H1) = C25×C13 · Schur multiplier (H2) = C29 |
| direct product | C13×#61052 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C13 | C23×D4 |
| commutator, Frattini, cosocle | C2×C4 | C25×C13 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C13 ◁ C13×#525 ◁ G | |
2722 conjugacy classes of subgroups.
| minimal degree | μ(G) = 49 |
| transitive degree | μt(G) = 832 |
A minimal faithful permutation representation — 5 generators on 49 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13)(14,15)(16,17)(18,19)(20,28)(21,25)(22,35)(23,26)(24,31)(27,36)(29,42)(30,39)(32,38)(33,46)(34,40)(37,44)(41,47)(43,49)(45,48);(18,20,23,32)(19,24,26,39)(21,29,34,45)(22,30,36,31)(25,37,40,49)(27,38,35,28)(33,43,47,44)(41,48,46,42);(15,17)(18,21,23,34)(19,25,26,40)(20,29,32,45)(22,33,36,47)(24,37,39,49)(27,41,35,46)(28,42,38,48)(30,43,31,44);(20,30)(22,36)(24,38)(27,35)(28,39)(29,43)(31,32)(33,47)(37,48)(41,46)(42,49)(44,45);(19,26)(24,39)(25,40)(27,35)(28,38)(37,49)(41,46)(42,48)754 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 54040);